Question

write the equation of the line that passes through the points (-3, -4) and (7, -2). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
For the points \((-3, -4)\) and \((7, -2)\), we have \( x_1=-3,y_1 = - 4,x_2 = 7,y_2=-2 \).
So \( m=\frac{-2-(-4)}{7-(-3)}=\frac{-2 + 4}{7 + 3}=\frac{2}{10}=\frac{1}{5} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use either of the two points. Let's use the point \((-3,-4)\) (we could also use \((7,-2)\)).
Substitute \( m = \frac{1}{5}\), \( x_1=-3 \) and \( y_1=-4 \) into the point - slope formula:
\( y-(-4)=\frac{1}{5}(x - (-3)) \)
Simplify the left - hand side and the right - hand side:
\( y + 4=\frac{1}{5}(x + 3) \)

Answer:

\( y + 4=\frac{1}{5}(x + 3) \) (or if we use the point \((7,-2)\), we get \( y+2=\frac{1}{5}(x - 7) \))